Question: Simplify the following expression: $ a = \dfrac{-6n + 4}{-3} + \dfrac{3}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-6n + 4}{-3} \times \dfrac{7}{7} = \dfrac{-42n + 28}{-21} $ Multiply the second expression by $\dfrac{-3}{-3}$ $ \dfrac{3}{7} \times \dfrac{-3}{-3} = \dfrac{-9}{-21} $ Therefore $ a = \dfrac{-42n + 28}{-21} + \dfrac{-9}{-21} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-42n + 28 - 9}{-21} $ $a = \dfrac{-42n + 19}{-21}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{42n - 19}{21}$